X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Focaml%2Ftactics%2FequalityTactics.ml;h=52ea4054de21ae6c0b2d1525f36398c114517e6e;hb=aca103d3c3d740efcc0bcc2932922cff77facb49;hp=a663282207c6057ae94cf4fdf4e7360bc74ba58f;hpb=296b163c8a2b09a6f87cbab15c2016de92fc8e70;p=helm.git diff --git a/helm/ocaml/tactics/equalityTactics.ml b/helm/ocaml/tactics/equalityTactics.ml index a66328220..52ea4054d 100644 --- a/helm/ocaml/tactics/equalityTactics.ml +++ b/helm/ocaml/tactics/equalityTactics.ml @@ -23,169 +23,133 @@ * http://cs.unibo.it/helm/. *) - -let rewrite_tac ~term:equality ~status:(proof,goal) = - let module C = Cic in - let module U = UriManager in - let curi,metasenv,pbo,pty = proof in - let metano,context,gty = List.find (function (m,_,_) -> m=goal) metasenv in - let eq_ind_r,ty,t1,t2 = - match CicTypeChecker.type_of_aux' metasenv context equality with - C.Appl [C.MutInd (uri,0,[]) ; ty ; t1 ; t2] - when U.eq uri (U.uri_of_string "cic:/Coq/Init/Logic/eq.ind") -> - let eq_ind_r = - C.Const - (U.uri_of_string "cic:/Coq/Init/Logic/eq_ind_r.con",[]) - in - eq_ind_r,ty,t1,t2 - | C.Appl [C.MutInd (uri,0,[]) ; ty ; t1 ; t2] - when U.eq uri (U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT.ind") -> - let eqT_ind_r = - C.Const - (U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT_ind_r.con",[]) - in - eqT_ind_r,ty,t1,t2 - | _ -> - raise - (ProofEngineTypes.Fail - "Rewrite: the argument is not a proof of an equality") - in - let pred = - let gty' = CicSubstitution.lift 1 gty in - let t1' = CicSubstitution.lift 1 t1 in - let gty'' = - ProofEngineReduction.replace_lifting - ~equality:ProofEngineReduction.alpha_equivalence - ~what:[t1'] ~with_what:[C.Rel 1] ~where:gty' - in - C.Lambda - (ProofEngineHelpers.mk_fresh_name context C.Anonymous ty, ty, gty'') - in - let fresh_meta = ProofEngineHelpers.new_meta proof in - let irl = - ProofEngineHelpers.identity_relocation_list_for_metavariable context in - let metasenv' = (fresh_meta,context,C.Appl [pred ; t2])::metasenv in - - let (proof',goals) = - PrimitiveTactics.exact_tac - ~term:(C.Appl - [eq_ind_r ; ty ; t2 ; pred ; C.Meta (fresh_meta,irl) ; t1 ;equality]) - ~status:((curi,metasenv',pbo,pty),goal) - in - assert (List.length goals = 0) ; - (proof',[fresh_meta]) -;; - - -let rewrite_simpl_tac ~term ~status = - Tacticals.then_ - ~start:(rewrite_tac ~term) - ~continuation: - (ReductionTactics.simpl_tac ~also_in_hypotheses:false ~terms:None) - ~status -;; - - -let rewrite_back_tac ~term:equality ~status:(proof,goal) = - let module C = Cic in - let module U = UriManager in - let curi,metasenv,pbo,pty = proof in - let metano,context,gty = List.find (function (m,_,_) -> m=goal) metasenv in - let eq_ind_r,ty,t1,t2 = - match CicTypeChecker.type_of_aux' metasenv context equality with - C.Appl [C.MutInd (uri,0,[]) ; ty ; t1 ; t2] - when U.eq uri (U.uri_of_string "cic:/Coq/Init/Logic/eq.ind") -> - let eq_ind_r = - C.Const - (U.uri_of_string "cic:/Coq/Init/Logic/eq_ind.con",[]) - in - eq_ind_r,ty,t2,t1 - | C.Appl [C.MutInd (uri,0,[]) ; ty ; t1 ; t2] - when U.eq uri (U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT.ind") -> - let eqT_ind_r = - C.Const - (U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT_ind.con",[]) - in - eqT_ind_r,ty,t2,t1 - | _ -> - raise - (ProofEngineTypes.Fail - "Rewrite: the argument is not a proof of an equality") - in - let pred = - let gty' = CicSubstitution.lift 1 gty in - let t1' = CicSubstitution.lift 1 t1 in - let gty'' = - ProofEngineReduction.replace_lifting - ~equality:ProofEngineReduction.alpha_equivalence - ~what:[t1'] ~with_what:[C.Rel 1] ~where:gty' - in - C.Lambda - (ProofEngineHelpers.mk_fresh_name context C.Anonymous ty, ty, gty'') - in - let fresh_meta = ProofEngineHelpers.new_meta proof in - let irl = - ProofEngineHelpers.identity_relocation_list_for_metavariable context in - let metasenv' = (fresh_meta,context,C.Appl [pred ; t2])::metasenv in - - let (proof',goals) = - PrimitiveTactics.exact_tac - ~term:(C.Appl - [eq_ind_r ; ty ; t2 ; pred ; C.Meta (fresh_meta,irl) ; t1 ;equality]) - ~status:((curi,metasenv',pbo,pty),goal) - in - assert (List.length goals = 0) ; - (proof',[fresh_meta]) - +let rewrite ~term:equality ?(direction=`Left) (proof,goal) = + let module C = Cic in + let module U = UriManager in + let module PET = ProofEngineTypes in + let module PT = PrimitiveTactics in + let module HLO = HelmLibraryObjects in + let if_left a b = + match direction with + | `Right -> b + | `Left -> a + in + let curi, metasenv, pbo, pty = proof in + let metano, context, gty = CicUtil.lookup_meta goal metasenv in + let eq_uri = HLO.Logic.eq_URI in + let ty_eq,_ = + CicTypeChecker.type_of_aux' metasenv context equality + CicUniv.empty_ugraph + in + let eq_ind, ty, t1, t2 = + match ty_eq with + | C.Appl [C.MutInd (uri, 0, []); ty; t1; t2] when U.eq uri eq_uri -> + let eq_ind = + C.Const (if_left HLO.Logic.eq_ind_URI HLO.Logic.eq_ind_r_URI,[]) + in + if_left (eq_ind, ty, t2, t1) (eq_ind, ty, t1, t2) + | _ -> raise (PET.Fail "Rewrite: argument is not a proof of an equality") + in + (* now we always do as if direction was `Left *) + let gty' = CicSubstitution.lift 1 gty in + let t1' = CicSubstitution.lift 1 t1 in + let gty'' = + ProofEngineReduction.replace_lifting + ~equality:ProofEngineReduction.alpha_equivalence + ~what:[t1'] ~with_what:[C.Rel 1] ~where:gty' + in + let gty_red = CicSubstitution.subst t2 gty'' in + let fresh_meta = ProofEngineHelpers.new_meta_of_proof proof in + let irl =CicMkImplicit.identity_relocation_list_for_metavariable context in + let metasenv' = (fresh_meta,context,gty_red)::metasenv in + let fresh_name = + FreshNamesGenerator.mk_fresh_name + ~subst:[] metasenv context C.Anonymous ~typ:ty + in + let pred = C.Lambda (fresh_name, ty, gty'') in + let exact_proof = + C.Appl [eq_ind ; ty ; t2 ; pred ; C.Meta (fresh_meta,irl) ; t1 ;equality] + in + let (proof',goals) = + PET.apply_tactic + (PT.exact_tac ~term:exact_proof) ((curi,metasenv',pbo,pty),goal) + in + assert (List.length goals = 0) ; + (proof',[fresh_meta]) + + +let rewrite_tac ~term = + let rewrite_tac ~term status = + rewrite ~term ~direction:`Right status + in + ProofEngineTypes.mk_tactic (rewrite_tac ~term) + +let rewrite_simpl_tac ~term = + let rewrite_simpl_tac ~term status = + ProofEngineTypes.apply_tactic + (Tacticals.then_ + ~start:(rewrite_tac ~term) + ~continuation: + (ReductionTactics.simpl_tac ~also_in_hypotheses:false ~terms:None)) + status + in + ProofEngineTypes.mk_tactic (rewrite_simpl_tac ~term) ;; - -let rewrite_back_simpl_tac ~term ~status = - Tacticals.then_ - ~start:(rewrite_back_tac ~term) - ~continuation: - (ReductionTactics.simpl_tac ~also_in_hypotheses:false ~terms:None) - ~status +let rewrite_back_tac ~term = + let rewrite_back_tac ~term status = + rewrite ~term ~direction:`Left status + in + ProofEngineTypes.mk_tactic (rewrite_back_tac ~term) + +let rewrite_back_simpl_tac ~term = + let rewrite_back_simpl_tac ~term status = + ProofEngineTypes.apply_tactic + (Tacticals.then_ + ~start:(rewrite_back_tac ~term) + ~continuation: + (ReductionTactics.simpl_tac ~also_in_hypotheses:false ~terms:None)) + status + in + ProofEngineTypes.mk_tactic (rewrite_back_simpl_tac ~term) ;; - -let replace_tac ~what ~with_what ~status:((proof, goal) as status) = +let replace_tac ~what ~with_what = + let replace_tac ~what ~with_what status = + let (proof, goal) = status in let module C = Cic in let module U = UriManager in let module P = PrimitiveTactics in let module T = Tacticals in - let _,metasenv,_,_ = proof in - let _,context,_ = List.find (function (m,_,_) -> m=goal) metasenv in - let wty = CicTypeChecker.type_of_aux' metasenv context what in - try - if (wty = (CicTypeChecker.type_of_aux' metasenv context with_what)) - then - let equality = - match CicTypeChecker.type_of_aux' metasenv context wty with - C.Sort C.Set -> "cic:/Coq/Init/Logic/eq.ind" - | C.Sort C.Type - | C.Sort C.CProp - | C.Sort C.Prop -> "cic:/Coq/Init/Logic_Type/eqT.ind" - | _ -> assert false - in - T.thens - ~start:( - P.cut_tac - (C.Appl [ - (C.MutInd ((U.uri_of_string equality), 0, [])) ; - wty ; - what ; - with_what])) - ~continuations:[ - T.then_ - ~start:(rewrite_simpl_tac ~term:(C.Rel 1)) - ~continuation:( - ProofEngineStructuralRules.clear - ~hyp:(List.hd context)) ; - T.id_tac] - ~status - else raise (ProofEngineTypes.Fail "Replace: terms not replaceable") - with (Failure "hd") -> raise (ProofEngineTypes.Fail "Replace: empty context") + let _,metasenv,_,_ = proof in + let _,context,_ = CicUtil.lookup_meta goal metasenv in + let wty,u = (* TASSI: FIXME *) + CicTypeChecker.type_of_aux' metasenv context what CicUniv.empty_ugraph in + let wwty,_ = CicTypeChecker.type_of_aux' metasenv context with_what u in + try + if (wty = wwty) then + ProofEngineTypes.apply_tactic + (T.thens + ~start:( + P.cut_tac + (C.Appl [ + (C.MutInd (HelmLibraryObjects.Logic.eq_URI, 0, [])) ; + wty ; + what ; + with_what])) + ~continuations:[ + + T.then_ ~start:(rewrite_simpl_tac ~term:(C.Rel 1)) + ~continuation:( + ProofEngineStructuralRules.clear + ~hyp:(List.hd context)) ; + T.id_tac]) + status + else raise (ProofEngineTypes.Fail "Replace: terms not replaceable") + with (Failure "hd") -> + raise (ProofEngineTypes.Fail "Replace: empty context") + in + ProofEngineTypes.mk_tactic (replace_tac ~what ~with_what) ;; @@ -195,51 +159,49 @@ let reflexivity_tac = IntroductionTactics.constructor_tac ~n:1 ;; - -let symmetry_tac ~status:(proof, goal) = +let symmetry_tac = + let symmetry_tac (proof, goal) = let module C = Cic in let module R = CicReduction in let module U = UriManager in let (_,metasenv,_,_) = proof in - let metano,context,ty = List.find (function (m,_,_) -> m=goal) metasenv in + let metano,context,ty = CicUtil.lookup_meta goal metasenv in match (R.whd context ty) with - (C.Appl [(C.MutInd (uri, 0, [])); _; _; _]) when (U.eq uri (U.uri_of_string "cic:/Coq/Init/Logic/eq.ind")) -> - PrimitiveTactics.apply_tac ~status:(proof,goal) - ~term: (C.Const (U.uri_of_string "cic:/Coq/Init/Logic/sym_eq.con", [])) - - | (C.Appl [(C.MutInd (uri, 0, [])); _; _; _]) when (U.eq uri (U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT.ind")) -> - PrimitiveTactics.apply_tac ~status:(proof,goal) - ~term: (C.Const (U.uri_of_string "cic:/Coq/Init/Logic_Type/sym_eqT.con", [])) + (C.Appl [(C.MutInd (uri, 0, [])); _; _; _]) + when (U.eq uri HelmLibraryObjects.Logic.eq_URI) -> + ProofEngineTypes.apply_tactic + (PrimitiveTactics.apply_tac + ~term: (C.Const (HelmLibraryObjects.Logic.sym_eq_URI, []))) + (proof,goal) | _ -> raise (ProofEngineTypes.Fail "Symmetry failed") + in + ProofEngineTypes.mk_tactic symmetry_tac ;; - -let transitivity_tac ~term ~status:((proof, goal) as status) = +let transitivity_tac ~term = + let transitivity_tac ~term status = + let (proof, goal) = status in let module C = Cic in let module R = CicReduction in let module U = UriManager in let module T = Tacticals in let (_,metasenv,_,_) = proof in - let metano,context,ty = List.find (function (m,_,_) -> m=goal) metasenv in + let metano,context,ty = CicUtil.lookup_meta goal metasenv in match (R.whd context ty) with - (C.Appl [(C.MutInd (uri, 0, [])); _; _; _]) when (uri = (U.uri_of_string "cic:/Coq/Init/Logic/eq.ind")) -> - T.thens - ~start:(PrimitiveTactics.apply_tac - ~term: (C.Const (U.uri_of_string "cic:/Coq/Init/Logic/trans_eq.con", []))) - ~continuations: - [PrimitiveTactics.exact_tac ~term ; T.id_tac ; T.id_tac] - ~status - - | (C.Appl [(C.MutInd (uri, 0, [])); _; _; _]) when (uri = (U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT.ind")) -> - T.thens + (C.Appl [(C.MutInd (uri, 0, [])); _; _; _]) + when (uri = HelmLibraryObjects.Logic.eq_URI) -> + ProofEngineTypes.apply_tactic + (T.thens ~start:(PrimitiveTactics.apply_tac - ~term: (C.Const (U.uri_of_string "cic:/Coq/Init/Logic_Type/trans_eqT.con", []))) + ~term: (C.Const (HelmLibraryObjects.Logic.trans_eq_URI, []))) ~continuations: - [T.id_tac ; T.id_tac ; PrimitiveTactics.exact_tac ~term] - ~status + [PrimitiveTactics.exact_tac ~term ; T.id_tac ; T.id_tac]) + status | _ -> raise (ProofEngineTypes.Fail "Transitivity failed") + in + ProofEngineTypes.mk_tactic (transitivity_tac ~term) ;;